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P(x)|Q(x) where both P,Q have coefficients of 1 or 2002

Source: Romanian TST 2002

February 5, 2011

algebrapolynomialnumber theory proposednumber theory

Problem Statement

Let

P(x)

and

Q(x)

be integer polynomials of degree

p

and

q

respectively. Assume that

P(x)

divides

Q(x)

and all their coefficients are either

1

2002

. Show that

p+1

is a divisor of

q+1

.
Mihai Cipu